I've tried running Linux Mint MATE on a live USB and while it will split long lines... it does not split a single word, like your "bluetooth" example photo. Its default is very clean and readable, maybe depending on screen resolution.
When you first installed MATE, did it not display properly for you too? If it did display properly, what settings have you tinkered with? I tried changing display resolution and changed to 200% scaling, but neither cause the icon text to be cut off in the middle of a word. Fractional scaling is not available on MATE.
If it worked well when first installed, you may consider reinstalling to fix it. Then keep a good Timeshift backup in case it goes sideways again.
If you want the icon text to be on a single line (no exceptions),
this thread may help. Changing the
text-ellipsis-limit from 3 to 1 (3 line limit to 1 line limit) will show icon text that looks like "GNU Imag..." with the long multiple-lines truncated by the ellipsis. This below worked on the live USB with Mint MATE. If you then click on a truncated text, it will highlight and show you the full text. You have to logout and log back in (or reboot) to see the change.
Code:
gsettings set org.mate.caja.desktop text-ellipsis-limit 1
Further fiddling around, I was able to "break" the icon text (not sure how) to the point where it cut off in the middle of the word to do the line wrap. The settings that I was fiddling with are in the file manager, Caja. Open Caja, go to Edit, then Preferences, then the Views tab (opens first for me)... down at the bottom there are Defaults for Icon View with various % options. Try changing to see if you find one that works. It seems strange the the file manager settings has an effect on the desktop, but it does... see
here and
here for reference.
Other options to try are to install
dconf-editor and/or
mate-tweak tools. They may provide something that will help. You may need some combination of settings above to get what you want, or return to what you want.
With
dconf-editor,
this article (updated Oct 2022) says you can reset the MATE desktop back to it's original defaults with just a single terminal command. If it works, it may save you the trouble of a full reinstall, but the article does caution that you will wipe out any other customizations that you have done.